Simplify. Remove all perfect squares from inside the square root. Assume $b$ is positive. $\sqrt{80b^2}=$
Explanation: Factor $80$ and find the greatest perfect square: $80=2\cdot 2\cdot 2\cdot 2\cdot 5=4^2\cdot 5$ The factor $b^2$ is a perfect square. $\begin{aligned} \sqrt{80b^2}&=\sqrt{4^2\cdot 5\cdot b^2} \\\\ &=\sqrt{4^2}\cdot \sqrt{5} \cdot \sqrt{b^2} \\\\ &=4\cdot \sqrt{5} \cdot b \\\\ &=4b\sqrt{5} \end{aligned}$